Infinite Body Centered Cubic Network of Identical Resistors
J. H. Asad
TL;DR
This paper derives the equivalent resistance between two points in an infinite BCC resistor network, providing exact formulas and asymptotic approximations for large distances, supported by numerical analysis.
Contribution
It presents a rational expression for the equivalent resistance in an infinite BCC resistor network, including asymptotic formulas for large separations.
Findings
Exact resistance formulas for the BCC network
Asymptotic resistance approximations for large distances
Numerical results validating the formulas
Abstract
We express the equivalent resistance between the origin and any other lattice site in an infinite Body Centered Cubic (BCC) network consisting of identical resistors each of resistance R rationally in terms of known values and . The equivalent resistance is then calculated. Finally, for large separation between the origin and the lattice site two asymptotic formulas for the resistance are presented and some numerical results with analysis are given.
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